The magnetic dipole moment on a spacecraft will produce a torque on the spacecraft due to the interaction of the dipole with the Earth's or another planet (such as Jupiter's) magnetic field. The magnetic dipole moment of a spacecraft may be due to current loops on the spacecraft or to permanent magnets on the spacecraft. The torque is computed from this equation:T=M×B  (Equation 1)
This equation dictates that torque (T) is the cross product between the magnetic dipole (M) and the Earth's or planet's magnetic field (B). This torque will cause the spacecraft to rotate. If such rotation is not desired, the torque will require compensation with another inertial torque in the opposite direction. An inertial torque is any torque that changes the spacecraft's angular momentum. The reference frame of the torque in the equation is the same as that of the dipole moment and the magnetic field. This torque produces an inertial torque on the spacecraft that will cause it to gain angular momentum over time. This angular momentum must be removed. For example, thrusters could be used to produce torques to compensate for this undesired torque. Solar pressure from the solar wings on a spacecraft with rotating wings could also be used to compensate for the torque due to a residual dipole, for example.
Generally, a magnetic dipole of a spacecraft is undesired from an attitude control point-of-view. Spacecraft designers make every effort to minimize these undesired magnetic dipoles. This torque only happens near planets with large magnetic fields such as the Earth or Jupiter. Many planets do not have magnetic fields. Some spacecraft take advantage of the magnetic field for control. They use rods made of magnetic steel that are wound with coils for control. These rods and coils form simple solenoids. An air coil torquer, which is a flat large area coil of wire, is another way of producing a control dipole.
When they are energized, that is current is passed through the coil, they produce a torque. However, due to hysteresis, even when off the magnetic core retains some magnetic dipole. Despite this, such magnetic torquers are used on geosynchronous satellites for control and for momentum unloading on other types of spacecraft.
Paluszek in U.S. Pat. No. 5,047,945 discloses a method for reducing attitude perturbations attributable to the interaction of magnetic fields of a heavenly body with those of a spacecraft which orbits thereabout that includes the steps of measuring the spacecraft momentum over a portion of an orbit of the spacecraft about the heavenly body, and measuring the body rate over the same portion of the orbit. Information is accessed which relates to the historic magnitude of the magnetic field of the heavenly body in the portion of the orbit, or the magnetic fields may be directly sensed. The magnitude and direction of the magnetic dipole of the spacecraft are estimated from at least the momentum, the body rate and the accessed or sensed information, to form an estimate of the magnetic dipole. This may be a direct estimate or inferred from the attitude motion of the spacecraft Current is passed through coils associated with the spacecraft in response to the estimate for tending to cancel the perturbations. This system is designed to cancel the residual dipole to reduce the disturbance torque. It has no provision for not perturbing the residual dipole and will not work if the residual dipole is not to be cancelled.